diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 5a057b48..0745ab48 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -27,7 +27,7 @@ jobs:
 
       - name: Install dependencies
         run: |
-          pip install "jupyterlab>=4.0.0,<5"
+          pip install "jupyterlab>=4.0.0,<4.2.0"
           pip install -e .
           jlpm
 
@@ -68,7 +68,7 @@ jobs:
 
       - name: Install dependencies
         run: |
-          pip install "jupyterlab>=4.0.0,<5"
+          pip install "jupyterlab>=4.0.0,<4.2.0"
           pip install -e .
           jlpm
 
@@ -103,7 +103,7 @@ jobs:
 
       - name: Install the Python dependencies
         run: |
-          python -m pip install "jupyterlab>=4.0.0,<5"
+          python -m pip install "jupyterlab>=4.0.0,<4.2.0"
           pip install -e ".[test]" codecov
 
       - name: List installed packages
@@ -216,7 +216,7 @@ jobs:
           mkdir test
           tar --strip-components=1 -zxvf *.tar.gz -C ./test
           cd test
-          python -m pip install "jupyterlab>=4.0.0,<5"
+          python -m pip install "jupyterlab>=4.0.0,<4.2.0"
           python -m pip install ".[test]"
           echo "::endgroup::"
 
diff --git a/jupyter_collaboration/rooms.py b/jupyter_collaboration/rooms.py
index d1e2a6bc..f92a5727 100644
--- a/jupyter_collaboration/rooms.py
+++ b/jupyter_collaboration/rooms.py
@@ -21,6 +21,8 @@
 class DocumentRoom(YRoom):
     """A Y room for a possibly stored document (e.g. a notebook)."""
 
+    _background_tasks: set[asyncio.Task]
+
     def __init__(
         self,
         room_id: str,
@@ -48,6 +50,7 @@ def __init__(
         self._cleaner: asyncio.Task | None = None
         self._saving_document: asyncio.Task | None = None
         self._messages: dict[str, asyncio.Lock] = {}
+        self._background_tasks = set()
 
         # Listen for document changes
         self._document.observe(self._on_document_change)
@@ -100,7 +103,10 @@ async def initialize(self) -> None:
             # try to apply Y updates from the YStore for this document
             read_from_source = True
             if self.ystore is not None:
-                await self.ystore.started.wait()
+                async with self.ystore.start_lock:
+                    if not self.ystore.started.is_set():
+                        self.create_task(self.ystore.start())
+                        await self.ystore.started.wait()
                 try:
                     await self.ystore.apply_updates(self.ydoc)
                     self._emit(
@@ -174,6 +180,11 @@ async def stop(self) -> None:
         self._document.unobserve()
         self._file.unobserve(self.room_id)
 
+    def create_task(self, aw):
+        task = asyncio.create_task(aw)
+        self._background_tasks.add(task)
+        task.add_done_callback(self._background_tasks.discard)
+
     async def _broadcast_updates(self):
         # FIXME should be upstreamed
         try:
diff --git a/pyproject.toml b/pyproject.toml
index 9e9c6cad..0898c0c8 100644
--- a/pyproject.toml
+++ b/pyproject.toml
@@ -29,7 +29,7 @@ classifiers = [
 dependencies = [
     "jupyter_server>=2.0.0,<3.0.0",
     "jupyter_ydoc>=2.0.0,<3.0.0",
-    "pycrdt-websocket>=0.13.2,<0.14.0",
+    "pycrdt-websocket>=0.13.4,<0.14.0",
     "jupyter_events>=0.10.0",
     "jupyter_server_fileid>=0.7.0,<1",
     "jsonschema>=4.18.0"
diff --git a/tests/conftest.py b/tests/conftest.py
index 943e2172..5f5a6a62 100644
--- a/tests/conftest.py
+++ b/tests/conftest.py
@@ -3,7 +3,7 @@
 from __future__ import annotations
 
 import json
-from asyncio import Event, sleep
+from asyncio import Event, create_task, sleep
 from datetime import datetime
 from typing import Any
 
@@ -177,7 +177,8 @@ def rtc_create_SQLite_store(jp_serverapp):
 
     async def _inner(type: str, path: str, content: str) -> DocumentRoom:
         db = SQLiteYStore(path=f"{type}:{path}")
-        await db.start()
+        task = create_task(db.start())
+        await db.started.wait()
 
         if type == "notebook":
             doc = YNotebook()